1. Limit Evaluation Set A (View Solutions for 1a - 1i)
1(a) \(\displaystyle \lim_{x \to 1 } \dfrac{x^2-1}{x-1}\)
1(b) \(\displaystyle \lim_{x \to -1 } \dfrac{x^2-1}{x+1}\)
1(c) \(\displaystyle \lim_{x \to 2 } \dfrac{x^2-4}{x-2} \)
1(d) \(\displaystyle \lim_{x \to 1 } \dfrac{x^2-3x+2}{2x-2}\)
1(e) \(\displaystyle \lim_{x \to -2} \dfrac{x^2+5x+6}{x^2+2x}\)
1(f) \(\displaystyle \lim_{x \to 3 } \dfrac{x^2-5x+6}{x^2-9}\)
1(g) \(\displaystyle \lim_{x \to \infty} \dfrac{2x^3-6x^2+5}{6x^3-3x+5}\)
1(h) \(\displaystyle \lim_{x \to \infty} \dfrac{2x^5-6x^2+5}{3x^4-3x+5}\)
1(i) \(\displaystyle \lim_{x \to- \infty} \dfrac{5x^4-6x+15}{2x^5-x^2+7}\)
2. Limit Evaluation Set B (View Solutions for 2a - 2e)
2(a) \(\displaystyle \lim_{x \to \frac{1}{2}} \left[ \cos (\pi x) - e^{x-\frac{1}{2}} \right]\)
2(b) \(\displaystyle \lim_{x \to -1}\frac{x^2-x-2}{7x+7}\)
2(c) \(\displaystyle \lim_{h \to 0}\frac{\sqrt{16+h}-4}{h}\)
2(d) \(\displaystyle \lim_{x \to 0}\dfrac{\frac{1}{x+4}-\frac{1}{4}}{x}\)
2(e) \(\displaystyle \lim_{x \to \infty} \dfrac{3x^5+5x+2}{2x^5-2x^3+1}\)